Mechanical impedance device



Dec. l16, 1930. P. B. FLANDERS 1,784,830

MECHANICAL IMPEDANCE DEVICE Y Filed Aug. 25, 1928 F/G. Z. /7 /6 /0 VVVVVV /NVENTOR Equi. B. FLANQFHS farro/*Neyl Patented Dec. 16, ,y 1930 UNITED STATES PATENT.. omer.

PAUL IB. FLANDERS, OF EAST ORANGE, NEW JERSEY, ASSIGNOR TO BELL TELEPHONE LABORATORIES, INCORPORATED, F NEW YORK, N. Y., A CORPORATION OF NEW YORK MECHANICAL IMPEDANCE DEVIICE Applicaties mea August 25, i928. serial No. 302,123.

This invention relates to impedance devices and more particularly to mechanical devices adapted to oppose to vibratory forces an impedance which is substantially constant and resistive.

Mechanical wave transmission lines, such as ilters and delay devices, have been designed for use in speech transmission systems, for example, as mechanical links .between two parts of an electrical line. rlhey may be incorporated into telephone systems by means of a mechanical-electrical translating device, such as a magnetic type of telephone receiver. In general, the mechanical lmpedancefof a receiver is not the same as the characteristic impedance ot'la mechanical line, and hence wave reflections occur at -the junction points. Thesel reflections give rise to irregularities in speech transmission which it is -desirable to avoid. The proper operation of such a combination requires that the mechanical line should receive wave energy from, and should deliver energy to, mechanical impedances equal to its characteristic impedance. This invention provides an adjustable mechanical impedance element which can be made to have an impedance equal to the characteristic impedance ,of a mechanical line, and so is Well adapted for the termination of mechanical wave transmission sys tems. The device consists essentially of an air chamber closed at one end by-a diaphragm and connected with theatmosphere at the other end through a narrow slot of air. The

slot has the nature' of a mechanical resistance, while. the diaphragm and air chamber are essentially a mass and elastanee, respectively. The linear dimensions oithe slot and lof the diaphragm, and the mass and elastance of the diaphragm and air chamber, are so proportioned-With respect to each other and to a preassigned resistance that the device has an impedance substantially constant and equal to the preassigned resistance over a wide range of frequencies. A feature of the invention is that the width of the slot is adjustable so that it can be made to have any impedance within its range ofadjustability.

The invention will bevunderstood from the following detailed descriptionv and by reference to the accompanying drawing of which Figs. 1 and 2 illustratethe invention; Fig. 3 shows the equivalent electrical circuit ofthe device; and Fig. 4 illustrates an application ot the invention in a mechanical vibratory system.

Fig. 1 shows a front view of the invention,

anLF ig. 2 is a side view in 'section showing the essential parts of the invention in its preferred form. The member, 10, is the base of the-device on which the other parts are assembled. The member, 11, Acomprises a threaded flange for screwing on the base, 10, and has integral with it a shaft with a conical end concentric with an aperture in the part, 10, into which it extends. These parts may be made of any workable material such Y as steel. A. diaphragm, 12, is held in place between two rings, 16 and 17, of asoft substance such as gum rubber which in turn are held in recesses inthe base piece by ametallic washer, 18, andan end piece, 19, which is threaded to screw into the base piece and which may conveniently have a pair of holes, 22, for applying a tool to aid in screwing into place. The diaphragm, which may be made of any light rigid metal, such as duralumin, has a rod, 15, attached at its center for connecting with the mechanical wave transmission line. The diaphragm is so shaped that its surface closely conforms to' tace of the member, 11. The width of the slot can be adjusted by screwing the flanged piece, 11, into or out ofthe base piece, 10. The outer chamber, 20, is in turn connected with the atmosphere by means of concentrioally centered holes, 21, in the piece, 11.l

The operation of the device can most readily be understood Afrom a study of its electrical analogue, which is illustrated in Fig. 3.

The diaphragm consists essentially of the 'nsI dimension of mass and is depicted as a series I inductance, M. The air chamber, 14,'consists of the element of stillness andis shown as a shunt condenser, S. Due to the fact that the efective areas of the diaphragm and of the)v annular slot. 13, are different, there is an iinpedance transformation,

where A2 is the eective diaphragm area and and is designed Z.

Fig. 4 is an illustration of the use of the presentinventioii as terminating elements for a mechanical line incorporated into a telephone system. A transmitter, 30, is shown connected through a transformer, 31, to a receiver, 32, the armature, 33, of which is rigidly` fastened to the terminating. elementv of a' mechanical line, 34. At the other end .of the line isconnected another translating device', 35, similar to the receiver, 32, for the purpose of .transforming the mechanical vibrations into electrical energy to send out on the electrical line, 36. Each endA of the mechanical line, 34, is connected to a terminating resistance unit, 37, of the form of this invention. The receiver and resistance unit are efetivel in series and since receivers of the type s own, in general, have impedances small in comparison lwith that of mechanical lines, the actual impedance terminating the line, 34, is approximately that 'of the terminating resistance unit; so no serious wave reflections occur, inasmuch 'as the ter.

minating unit is made to have a resistance equal to the characteristic impedance of the` mechanical line.

. It remains to show how avterminating elel ment embodying this invention can be designed in accordance with a given resistance value. The impedance of a parallel-sided slot, such as the slot, 13, is given by the equation,

in which,

,a is the coelicient of viscosity, p the air density, d the width of the slot between the walls, b the length of the slot transverse'to the direction of flow, and l Z the length in the direction of flow. The dimensions of Z when c.g. s. units are used, are

dyne seconds 0 centimeters ipsrsso The impedance Z is the mechanical impedance, delined as the ratio of the total pressure Y that the reactance be less than 10% of the resistance at all frequencies up to an assigned limiting frequency, mOi-2n, the separation should be at least as small as that given by If d be apiroximately .001 the impedance lwill ybe su stantially free from reactance throughout the range of speech frequencies. The edect of viscosity in producing a sliding or shearing motion of the adjacent layers oi" vair with respect to each other, is discussed in From this it follows that the separation dclined by Equation (2) is approximately oneninth of the shear velocity wave, or diffusion wave, corresponding to the highest frequency to be considered. In calculating the effect of inserting a resistance device into any given soundconduit, it is necessary to take into account the transformer effect due to the difference between the cross-sectional areas of the air paths in the element and in the conduit. A more detailed discussion of impedance transformations involved when air chambers'of different cross-sectional areas are joined, is given in a paper by H. C. Harrison and J. P. Maxfield entitlted Methods of high quality recording and reproducing of music and speech based on telephone research in the American Institute of Electrical Engineers Journal, February, 1926, pages 334-348. In Fig. 2 the annular air slot, 13, is a resistance element substantially free from reactance because the width, d, between the walls is very narrow. Its length, Z, is as shown in the figure. The length of the passage transverse to the direction of air flow, b, is approximately 2n', where o is the mean radius of the slot, and its area, A1, transverse to the direction of flow is approximately 2nd. The diaphragm illustrated is the plunger type in which tlie'central part out to the radius r, is rigid and the portion between the radii 7'1 and 1'2 is flexible. The radii r1 and r2 are shown inthe figure. The

edective area for the present purpose of this type of diaphragm is given by the equation,

and should be made equal to the characteristie impedance of the mechanical line. The

mass of the diaphragm, M, and the stiffness of the air chamber, S, constitute a portion of low pass filter and consequently must be so proportioned with respect to Za that the characteristic impedance is the saine. Furthermore, there will be a cut-off frequency above which attenuation occurs, and which must be so located, that the desired band of frequencies is transmitted. In Eig. 4 the. mechanical line consists of masses, 88, effectively in seriesand springs or elastance's, 39, effectively in shunt, and hence is a low pass filter. The mass, M, and stiffness, S, of the terminal device should preferably be proportionecl to effectively constitute part of the filter. Then the terminating mass of the filter With the diaphragm mass, M, together. constitute a full section mass. Likewise, the stiffness, S, should preferably be twice that of each. spring of the mechanical filter so that the filter will be effectively mid-shunt terminated in accordance With the theory of filter design. For a treatment of this theory reference is made to Chapters XVI and XVII of Transmission Circuits for Telephoniel Communication by K. S. Johnson, published by D. Van Nostrand Co., Incorporated. -It is not essential, however, that M and vS be treated as a component part of the line with which the'device is used. Satisfactory operation is obtained so long as. the cut-off frequency of M and S considered as ahalf section of low pass filter, is situated-substantially above the range of frequencies being transmitted. The above reference to K. S. Johnson treats of the theory of half sections of filters. In taking into account the mass of the diaphragm, an effective mass must be used which for the corrugated plunger type diaphragm shown in the drawing is e217- pressed by,

where MW is the weighed mass. When M and S are the mass and stiffness of a half section, the cut-off frequency fc, is given by,

#2in/gg, u)

and the characteristic impedanceis,

l i where The impedance of the slot,13, asl seen from cA2 y" k=coeficient of elasticity of air=l.4 106 c. g. s. units,

V=volume of air chamber in c. g. s. units. -In c. g. s. units M is measured in grams, S in dynes per centimeter and K in dyne sec-I onds per centimeter.

In designing a resistance unit in accordance with the invention, it is preferable to start by assigning convenient values to the diameter and length of the annular air slot. Its impedance can then be adjusted by means of the variable Width, d, in accordance with Equation The effective area vof the diaphragm, A2, may then be established so that Za., accordi-ng to Equation (5), has the value prefassigned to the device. This is done by assigning proper values to the radii r1 and r2 as shown by Equation 4. By the choice of a material and thickness "for the diaphragm, its Weight is determined, from which its effective mass is ascertained from Formula. (6). It is necessary then, to fix the air chamber volume, V, so that the proper value ofelasticity, S, is obtained to make the characteristic impedance, K, equal to Ze by Equation (8) If it should be found that this elasticity, when applied to Formula 7, gives too low a Value for the cut-ofia frequency', the diaphragm may be made thinner, which will result in a smaller mass, M, and necessitate a larger elastance, S. When the impedance, Z4., is varied by regulating the width of the annular slot, 'the characteristic impedance, K, should vary equally. This Will follow if the slot Width, d, is proportional to the square of the air chamber volume, V. as the member, 11, is moved in and out of the base piece, 10. This condition holds approximately when the following dimensions are employed or When their same proportions are adhered to:

- restricted to these features, but only in accordance with the appended claims. The

form disclosed is advantageous, however, be-

lcause of the added rigidity of the corrugated,

tvpe diaphragm and because the resultant s ape of the air chamber allows the ilow of air to occur lthrough the annular slot without lexcessive eddies of air currents.

l. A mechanical resistance unit comprising'a diaphragm for receivingenergy from a vibratory system,'an air chamber, and means defining slot through which occurs a flow of air between said chamber and the atmosphere due to vibrations of said diaphragm, said slot being narrow in a direction transverse to that of the air flow and having an appreciable length in the direction of flow, whereby it offers an impedance to the air iow which is substantially a resistance free from reactance. a

2. A mechanical resistance unit for damping vibratory waves, said unit comprising a corrugated diaphragm, an air chamber, and means defining an annular slot the diameter of which is approximately equal to and coincident with that of a ridge of said diaphragm, the motion of said diaphragm being damped by forcing air into and out of said air chamber through said slot, said slot being narrow and having an appreciable length in the direction of air flow wherebyit oiers to the yiiow of air an impedance which 1s substantially a resistance free from react- 3. A mechanicalresistance unit for damping mechanical vibrations comprising a base piece, a member extending through an aperture in said base piece, there being a very narrow space'between the surfaces of said member and of said aperture, and a diaphragm having a shape conforming'to the inner surfaces of said base piece and of said member and held in proximity thereto.

4. A mechanical resistance unit comprising a diaphragm, air chamber, and means delining a-'slot through which air is forced into and o'ut of said air chamber by vibration of'said diaphragm, said slot being narrow in a direction transverse to that of air low and having an appreciable length in the direction of flow whereby it oii'ers a 'resistive impedance substantially free fromV reactance to the air ow; the width of said slot being adjustable.

5. A mechanicalresistance unit comprising a base piece havingan aperturewith a conical surface, a member with a conical surface protruding through said aperture, leaving-a vnarrow annular space between said Y Surfaces, and a diaphragm havin a corrugated area closely conforming in s ape with' the inner areas of said base piece and conical inasso member and fastened in such a manner that it encloses an air chamber, said conical member being movable inward and outward through said aperture so that the width of said annularspace and the volume of said air chamber may be varied.

6. A mechanical resistance unit in accordance with claim 5 in which the movement of the conical member causes the width of the narrow annular slot to vary proportionally to the square of the air chamber volume.

In witness whereof, hereunto subscribe my name this 22nd day of August, 1928.

. PAUL B. AFLANZDERS. 

